http://dx.doi.org/10.1090/pspum/032.2
PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume XXXII, Part 2
ALGEBRAIC AND GEOMETRIC TOPOLOGY
AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1978 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY
HELD AT STANFORD UNIVERSITY STANFORD, CALIFORNIA AUGUST 2-21, 1976 EDITED BY R. JAMES MILGRAM
Prepared by the American Mathematical Society with partial support from National Science Foundation grant MCS 76-01696
Library of Congress Cataloging in Publication Data
Symposium in Pure Mathematics, Stanford University, 1976. Algebraic and geometric topology. (Proceedings of symposia in pure mathematics; v. 32) "Proceedings of the Symposium in Pure Mathematics of the American Mathema• tical Society, held at Stanford University, Stanford, California, August 2—21, 1976." Bibliography: v. 1, p. v. 2, p. 1. Algebraic topology—Congresses. 2. Manifolds (Mathematics)—Congresses. 3. Global analysis (Mathematics)—Congresses. I. Milgram, R. James. II. American Mathematical Society. III. Title. IV. Series. QA612.S93 1976 514'.2 78-14304 ISBN 0-8218-1432-X (v. 1) ISBN 0-8218-1433-8 (v. 2)
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The American Mathematical Society held its 24th Summer Research Institute at Stanford University from August 2-21, 1976. The topic of the meeting was Alge• braic and Geometric Topology. Particular emphasis was placed on Algebraic K- and L-Theory, Surgery and Surgery Classifying Spaces, Group Actions on Mani• folds, and 3 and 4 Manifold Theory. The organizing committee consisted of Raoul Bott, William Browder (Co- chairman), Pierre Conner, Robion Kirby, Richard Lashof, R. James Milgram (Chairman), Daniel Quillen, and P. Emery Thomas (Co-chairman). The main lecturers were Raoul Bott, Richard Lashof and Mel Rothenberg, Syl- vain Cappell and Julius Shaneson, C. McA. Gordon, Robert Edwards, Allen Hatcher and Jack Wagoner, Wu. C. Hsiang, Max Karoubi, R. James Milgram, Daniel Quillen, Laurence Siebenmann, and C. T. C. Wall. Special hour lectures were given by Gregory Brumfiel, William Jaco, Robion Kirby, Ronnie Lee, James Lin, lb Madsen, John Morgan, Robert Oliver, Ted Petrie, P. Emery Thomas, F. Waldhausen, and James West. There was also a series of problem sessions run by Raoul Bott (foliations), W. C. Hsiang (group actions and surgery), R. Kirby (3 and 4 manifolds), and C. T. C. Wall (algebraic K- and £-theory). Among the more active seminars were 3 and 4 manifolds (Kirby), Kervaire in• variant (Browder—E. Brown), Homotopy theory (E. Thomas—M. Mahowald), Algebraic K- and L- theory (J. Wagoner), Group actions (W. C. Hsiang), Folia• tions (Bott), Geometry of manifolds (L. Siebenmann), and Surgery and surgery classifying spaces (R. Lashof). These proceedings include write ups of most of the main lectures, as well as selected seminar talks, and most of the problem sessions. The institute was sponsored by the National Science Foundation under contract number MCS 76-01696. The organizing committee wishes to thank Dorothy Smith of the American Mathematical Society for her help in running and organizing the conference.
R. JAMES MILGRAM STANFORD UNIVERSITY
ni TABLE OF CONTENTS
Structure of Topological Manifolds
TAKAO MATUMOTO, Triangulation of manifolds 3 DAVID E. GALEWSKI AND RONALD J. STERN, Simpiicial triangulations of topological manifolds 7 ALLAN L. EDMONDS, Fibering topological manifolds ..13
Low Dimensional Manifolds
FRIEDHELM WALDHAUSEN, Recent results on sufficiently large 3-manifolds 21 A. J. CASSON AND C. MCA. GORDON, On slice knots in dimension three 39 JOHN R. STALLINGS, Constructions of fibred knots and links ...55 HUGH M. HILDEN AND JOSE M. MONTESINOS, A method of constructing 3-manifolds and its application to the computation of the /^-invariant 61 WILLIAM JACO AND PETER B. SHALEN, A new decomposition theorem for irreducible sufficiently-large 3-manifolds 71 MICHAEL FREEDMAN AND ROBION KIRBY, A geometric proof of Rochlin's theorem .85 YUKIO MATSUMOTO, Secondary intersectional properties of 4-manifolds and Whitney's trick ...99
Geometry of Differential Manifolds and Algebraic Varieties
E. REES AND E. THOMAS, Smoothings of isolated singularities ....Ill JOHN O. MORGAN, Hodge theory for the algebraic topology of smooth algebraic varieties ....119 SYLVAIN E. CAPPELL AND JULIUS L. SHANESON, An introduction to embeddings, immersions and singularities in codimension two 129 DONALD DAVIS AND MARK MAHOWALD, Immersions of projective spaces 151 WILLIAM D. HOMER, Singularities in lens spaces ..155 FRANZ W. KAMBER AND PHILIPPE TONDEUR, Characteristic classes and Koszul complexes ....159 WENSOR LING, Translations on M x R ... 167 WALTER D. NEUMANN, Homotopy invariance of Atiyah invariants .....181 HERBERT SHULMAN, Covering dimension and characteristic classes for foliations 189 JOHN W. WOOD, A connected sum decomposition for complete intersections 191 STEPHEN SHING-TOUNG YAU, Normal singularities of surfaces. 195
v VI TABLE OF CONTENTS
//-Spaces, Loop Spaces, and CW Complexes
JAMES P. LIN, On the topology of finite /f~spaces 201 JOHN R. HARPER, On the construction of mod p /2-spaces 207 ERIK KJAER PEDERSEN, Smoothings of ff-spaees 215 PETER J. KAHN, The homotopy-dimension of nilpotent spaces 217 JOEL M. COHEN, Complexes of cohomological dimension two. 221 F. R. COHEN, M. E. MAHOWALD AND R. J. MILGRAM, The stable decomposition for the double loop space of a sphere 225 J. P. MAY, H^ ring spectra and their applications .....229 F. R. COHEN, Little cubes and the classifying space for w-sphere fibrations ...245
Problems
W. BROWDER AND W. C. HSIANG, Some problems on homotopy theory, manifolds and transformation groups .251 COMPILED BY MARK MOSTOW AND PAUL SCHWEITZER, Foliation problem session (R. Bott)..... 269 ROB KIRBY, Problems in low dimensional manifold theory 273 FRIEDHELM WALDHAUSEN, Some problems on 3-manifolds 313